A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results were as follows: 31 said they drove alone, 39 rode in carpool, 35 rode public transportation, 10 used both carpool and public transportation, 7 used both a carpool and sometimes their own cars, 9 used buses as well as their own cars, 5 used all three methods. how many used none of the above-mentioned means of transportation?

Question

A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results were as follows: 31 said they drove alone, 39 rode in carpool, 35 rode public transportation, 10 used both carpool and public transportation, 7 used both a carpool and sometimes their own cars, 9 used buses as well as their own cars, 5 used all three methods. how many used none of the above-mentioned means of transportation?

Answer 1

Make a Venn diagram, showing three overlapping circles, label them

A for driving alone
C for carpool
P for public trans

put 5 in the intersection of all 3 circles
10 used C and P, so 10 goes in that intersection, BUT 5 are already counted, so place 5 in the outer part of the intersection of C and P
in the same way, place 4 in the outer part of A and P
in the same way , place 2 in the outer part of A and C
now each circle itself
A should have a total of 31, but I already have 11 counting in the A circle, leaving 20 in the unused part of A
C should have 39, but I already have 12 filled in, leaving 27 for the rest of circle C
P should have 35, but I already have 14 filled in, leaving 21 for the rest of circle P

Adding up all the numbers I see filled in, I get 84
so from the 100 students, 16 do not use any of the 3 methods.

check my arithmetic

Answer 2

N(A and C and P)

= N(A) + N(C) + N(P) - N(A and C) - N(A and P) - N(C and P) + N(A and C and P)
= 31 + 39 + 35 - 10 - 7 - 9 + 5
= 84

so 100 - 84 are unaccounted for
16 don't use any of the given ways

Answer 3

To find out how many students used none of the mentioned means of transportation, we need to subtract the total number of students who used any form of transportation from the total number of students in the poll.

Let's break down the information given:

- 31 students said they drove alone.
- 39 students rode in a carpool.
- 35 students rode public transportation.
- 10 students used both carpool and public transportation.
- 7 students used both a carpool and their own cars.
- 9 students used buses as well as their own cars.
- 5 students used all three methods.

To get the total number of students who used any form of transportation, we need to add up the numbers for each group:

31 + 39 + 35 + 10 + 7 + 9 + 5 = 136 students.

Now, to find the number of students who didn't use any of the mentioned means of transportation, we subtract the total number of students who used transportation from the total number of students in the poll:

100 - 136 = -36.

Since we can't have a negative number of students, it appears there is an issue with the data. Therefore, it seems there was an error in the question or the given information.